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We all know about division using decimals and places, you just keep dividing each digit place and move on to the next one.

I was wondering if there was a similar method by which you could manually take a root or exponents where you start with one digit place and move on to the right.

Simply Beautiful Art
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  • I'm sure there is one for roots, as I remember seing it in high school. For exponentiation, repeated squaring is easy to do on paper, and you can think of it as being "digit-by-digit" if you work in base two. – xyzzyz Feb 23 '16 at 01:02
  • @xyzzyz hm, that is interesting. I have yet to see that done before. I think the squaring in base two is probably very interesting. – Simply Beautiful Art Feb 23 '16 at 01:06
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    google: extract square root with pencil and paper . some results: http://www.homeschoolmath.net/teaching/square-root-algorithm.php , http://mathforum.org/library/drmath/view/52605.html , http://www.maa.org/press/periodicals/convergence/extracting-square-roots-made-easy-a-little-known-medieval-method-al-hassar-s-description-of-the-0 – Mirko Feb 23 '16 at 01:07
  • @Mirko Thanks! That pretty much answers my question. – Simply Beautiful Art Feb 23 '16 at 01:09
  • you are welcome, note one of the above links is about cube (not square) roots. Here are a couple more links, the second of which shows your question is a duplicate: http://www.davdata.nl/math/root.html , http://math.stackexchange.com/questions/90435/how-can-i-find-the-square-root-using-pen-and-paper And one extra link, to Wikipedia (copied from the other MSE question), different methods https://en.wikipedia.org/wiki/Methods_of_computing_square_roots – Mirko Feb 23 '16 at 01:14
  • @Mirko Since OP found them useful, perhaps you could develop your comments into an answer? – Travis Willse Feb 23 '16 at 10:29

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